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In this note we point out some errors in the paper "On the set of solutions for the Darboux problem for fractional order partial hyperbolic functional differential inclusions" by S. Abbas and M. Benchohra published in Fixed Point Theory, vol. 14, no. 2, 2013, 253-262. [ABSTRACT FROM AUTHOR]

In the paper "AIMS Math. 5 (2020), no. 6, 6448-6456", Tian et al. [15, Theorem 1] considered a linear system of integro-time delay differential equations (IDDEs) with constant time retardation. In [15], firstly, a generalized double integral inequality was obtained and then less conservative asymptotically stability criteria were proposed by using that double integral inequality and choosing a new Lyapunov-Krasovskii functional (LKF). To the best of the information, we would like to note that the asymptotically stability criteria of Tian et al. [15, Theorem 1] consist of very interesting but strong conditions. However, in this paper, we define a more suitable LKF, then we obtain the result of Tian et al. [15, Theorem 1] for uniformly asymptotically stability under very weaker conditions using the LKF and also investigate the integrability of the norm and boundedness of solutions. To show the effectiveness of our results, two numerical examples are proposed for the uniformly asymptotically stability as well as integrability and boundedness of solutions. By this work, we do contributions to the work of Tian et al. [15, Theorem 1] under very weaker conditions and those in the previous relevant literature, and we obtain two more new results on the integrability of the norm of solutions and boundedness of solutions. The results of this paper are new and they may be useful for researchers working on the topics of this paper. [ABSTRACT FROM AUTHOR]

A new iterative algorithm is proposed for finding a common solution of an equilibrium problem and a fixed point problem. Then, a strong convergence theorem is proved. As a consequence, they can be obtained some strong convergence theorems for an equilibrium problem and a split common fixed point problem. The obtained theorems can be applied to solve an equilibrium problem and a split common null point problem. The results presented in this paper extend and improve some corresponding ones in the literature. Finally, a numerical example is given to show the validity of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we study the following Schrödinger-Kirchhoff type equations involving the fractional p-Laplacian ... and H(x), we obtain the existence of positive ground state solutions and discuss their asymptotical behavior via the method used by Bartsch and Wang [Multiple positive solutions for a nonlinear Schrödinger equation. Z. Angew. Math. Phys. 51 (2000) 366-384]. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the nonemptiness and boundedness of the set of zeros of a monotone operator in Hadamard spaces. Two coercivity conditions R1 and R2 are proposed. The equivalence between the nonemptiness of the set of zeros of a monotone operator and coercivity condition R1 is established. Moreover, it is shown that coercivity condition R2 is a su_cient and necessary condition for the boundedness of the set of zeros of a monotone operator. Some applications in convex minimization and fixed point theory are also presented to support the main results. [ABSTRACT FROM AUTHOR]

In this paper, a self-adaptive algorithm involving inertial technique will be introduced to solve bilevel pseudo-monotone variational inequality problems in Hilbert spaces. The main advantages of our algorithm is that the strong convergence theorem of the stated iterative method is proved without Lipschitz continuity condition of the associated mapping. Finally, the effectiveness and superiority of the proposed algorithm are proposed by numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, we consider the notion of generalized multi-valued F contraction mappings and prove fixed point theorems for this type mappings. Finally, we construct non-trivial example to validate the potential of our result. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the new notion of generalized α-φ-Geraghty proximal contraction mappings and investigate the existence of the best proximity point for such mappings in complete metric spaces. The obtained results extend, generalize, and complement some known fixed and best proximity point results from the literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish a general fixed point theorem for mean nonexpansive multivalued mappings defined on weakly compact and convex subsets of Banach spaces with property (D). The main result obtained in this paper significantly extends and improves many of the well-known results in the existing literature. [ABSTRACT FROM AUTHOR]

In their recent papers, A.V. Arutyunov and A.V. Greshnov introduced (q1; q2)-quasimetric spaces and studied their properties: investigated covering mappings between (q1; q2)- quasimetric spaces, established sufficient conditions for the existence of a coincidence point for two mappings acting between (q1; q2)-quasimetric spaces such that one is a covering mapping and the other is Lipschitz continuous, proved Banach's fixed point theorem, obtained generalizations for multivalued mappings. The class of (q1; q2)-quasimetric spaces is sufficiently wide; it includes quasimetric spaces, b-metric spaces, Carnot-Caratheodory spaces with Box-quasimetics, Lp-spaces with p 2 (0; 1), etc. The development of the theory of coincidence points of mappings on (q1; q2)- quasimetric spaces initiated interest in the study of more general f-quasimetric spaces and in generalizing Banach's fixed point theorem to such spaces. The present paper is a review of these results. [ABSTRACT FROM AUTHOR]

In this paper we give some fixed point theorems for nonself operators on a large Kasahara space, which generalize some results given by I.A. Rus and M.-A. Sérban (I.A. Rus, M.-A. Serban, Some fixed point theorems for nonself generalized contractions, Miskolc Math. Notes, 17(2016), no.2, 1021-1031) and by S. Reich and A.J. Zaslavski (S. Reich, A.J. Zaslavski, A note on Rakotch contractions, Fixed Point Theory, 9(2008), no.1, 267-273). [ABSTRACT FROM AUTHOR]

In this paper we study the existence of multiple nontrivial positive weak solutions to the following system of problems. We will guarantee the existence of a solution in the Nehari manifold. Further by using the Lusternik-Schnirelman category we will prove the existence of at least cat(?) + 1 number of solutions. [ABSTRACT FROM AUTHOR]

In this paper, by using the Guo-Krasnoselskii theorem, we investigate the existence and nonexistence of positive solutions of a class of boundary value problem of third-order nonlinear differential equation involving Stieltjes integral conditions. Under some growth conditions imposed on the nonlinear term, we obtain explicit ranges of values of parameters with which the problem has a positive solution and has no positive solution respectively. An example is given to illustrate the main results of the paper. [ABSTRACT FROM AUTHOR]

In this paper, we study a viscosity approximation method for finding a nearest fixed point of a continuous pseudo-contraction mapping in a Hadamard space. We applied our result to solve some convex minimization problems. We also present an example to validate our new findings. This work substantially improves and generalizes some well-known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper we obtain nonlinear alternatives of Leray-Schauder and Mönch type for nonself vector-valued operators, under hybrid conditions of Perov contraction and compactness. Thus, we give vector versions of the theorems of Krasnosel'skii, Avramescu, Burton-Kirk and Gao-Li-Zhang. An application is given to a boundary value problem for a system of second order differential equations in which some of the equations are implicit. [ABSTRACT FROM AUTHOR]

The purpose of this paper is concerned with the approximate solution of split equality problems. Two types of CQ algorithms with a new self-adaptive stepsize criterion are presented without prior knowledge of operator norms. The corresponding strong convergence theorems are obtained under mild conditions. Moreover, some numerical examples including an application in signal recovery problems, are provided to show the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, four extragradient-type algorithms are presented for solving bilevel variational inequalities of pseudomonotone and non-Lipschitz continuous operators in real Hilbert spaces. The proposed iterative schemes employ two Armijo-type linesearch methods making them work adaptively. Strong convergence theorems of the suggested algorithms are established under some mild conditions. Finally, some numerical experiments and applications are given to verify the advantages and efficiency of the proposed algorithms over some previously known ones. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new algorithm for solving split feasibility problems in Hilbert spaces. The algorithm stems from the relaxed CQ method and the alternated inertial step method. The proposed algorithm uses variable step-sizes which are updated at each iteration by a cheap computation without linesearch. This step-size rule allows the resulting algorithm to work more easily without the prior knowledge of the operator norm. Numerical experiments are implemented to illustrate the theoretical results and also to compare with existing algorithms. [ABSTRACT FROM AUTHOR]

Let X be an arbitrary topological space and g : X x X → R be a real valued continuous function defined on X x X. In this article, we introduce two notions like topologically Berinde weak proximal contraction and topologically proximal weakly contractive mapping with respect to g. We explore sufficient conditions for the existence and uniqueness of best proximity points for these classes of mappings. Moreover, in the last part of the paper, we show that the best proximity point theorem for topologically proximal weakly contractive mapping can be deduced from some fixed point theorems in topological spaces. [ABSTRACT FROM AUTHOR]

Let C be a nonempty closed bounded (not necessary convex) subset of a Banach space X and let T : C → C be an (αβ)-nonexpansive mapping with α > 0, β > 0 and α + β < 1. In this paper, we show that T has a unique fixed point. Moreover, T is a Picard operator if and only if T is asymptotically regular. [ABSTRACT FROM AUTHOR]

In this paper, we give some further comments to the counterexample and the results of Bisht in [R.K. Bisht, Comment on: A new fixed point theorem in the fractal space, Indagationes Mathematicae, 29(2018), no.2, 819-823.]. [ABSTRACT FROM AUTHOR]

This paper focus on the class of multivalued iterated contractions, mappings which are contractive throughout the orbits. We show that the proof of Nadler's theorem still holds for these mappings whenever they satisfy a rather weak type of continuity, which gives us a new fixed point theorem. We show several types of mappings that properly contain Suzuki (C)-typ e generalized contraction mappings and for which our fixed point results apply. We conclude the paper showing some further examples of iterated contraction mappings which are, respectively, the mappings satisfying condition (B) and an extension to the multivalued case of mean iterated contractions and we also obtain fixed point results for these classes of mappings. [ABSTRACT FROM AUTHOR]

In this paper, we study split common fixed point problems of Bregman demigeneralized and Bregman quasi-nonexpansive mappings in reflexive Banach spaces. Using the Bregman technique together with a Halpern iterative algorithm, we approximate a solution of split common fixed point problem and sum of two monotone operators in reflexive Banach spaces. We establish a strong convergence result for approximating the solution of the aforementioned problems. It is worth mentioning that the iterative algorithm employ in this article is design in such a way that it does not require prior knowledge of operator norm and we do not employ Fejer monotinicity condition in the strategy of proving our convergence theorem. We apply our result to solve variational inequality and convex minimization problems. The result discuss in this paper extends and complements many related results in literature. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of abstract fractional differential inclusion with finite delay in which the multi-valued nonlinearity is possibly superlinear. We analyze some sufficient conditions that ensure the global solvability of problem. Our main result is the existence of a compact set of decay solutions to our problem by estimating the measure of noncompactness and using the fixed point theory for a condensing map. The obtained results will be applied to a concrete polytope fractional differential system. [ABSTRACT FROM AUTHOR]

Stochastic production planning problems were studied in several works; the model with one production good was discussed in [3]. The extension to several economic goods is not a trivial issue as one can see from the recent works [8], [9] and [13]. The following qualitative aspects of the problem are analyzed in [9]: the existence of a solution and its characterization through dynamic programming/Hamilton Jacobi Bellman (HJB) equation, as well as the verification (i.e., the solution of the HJB equation yields the optimal production of the goods). In this paper, we stylize the model of [8] and [9] in order to provide some quantitative answers to the problem. This is possible especially because we manage to solve the HJB equation in closed form. We point to a fixed point characterization of the optimal production rates. Among other results, we find that the optimal production rates adjusted for demand are the same across all the goods and they also turn to be independent of some model parameters. Moreover we show that production rates (adjusted for demand) are increasing in the aggregate number of goods produced, and they are also uniformly bounded. Numerical experiments show some patterns of the output. [ABSTRACT FROM AUTHOR]

In this paper, we introduce α-nonexpansive multi-valued mappings in Hilbert spaces, and prove some properties and the existence of fixed points of these mappings. Further, we apply the Fan-KKM theorem to prove the existence of solutions to split equilibrium problems. Then we study iterative schemes for solving split equilibrium problems and common fixed point problems of a finite family of α-nonexpansive multi-valued mappings in Hilbert spaces. we prove that the proposed iterative algorithms converge weakly and strongly to a common solution of the considered problems. Our results improve and extend the previous results given in the literature. [ABSTRACT FROM AUTHOR]

In this paper the Halpern type S-iteration process introduced by D. R. Sahu is further analyzed for different class of nonlinear nonexpansive mappings in uniformly convex Banach space. [ABSTRACT FROM AUTHOR]

In this paper, a viscosity splitting iterative algorithm with perturbation is introduced for solving an inclusion problem with two accretive operators and a fixed point problem of an infinite family of nonexpansive mappings. Strong convergence of the iterative algorithm is obtained in a Banach space. A convex minimization problem is also considered in Hilbert spaces as an applications. [ABSTRACT FROM AUTHOR]

In this paper, we first state and establish some general existence theorems in Hadamard spaces. Then, we introduce class of λ-hybrid mappings in Hadamard spaces and prove existence of fixed point for such mappings. Finally, we establish convergence theorem of Mann's iterative process for λ-hybrid mappings. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence and uniqueness of solutions to boundary value problem for differential equations with generalized Hilfer type fractional derivative. The arguments are based upon the Banach contraction principle and Krasnoselskii's fixed point theorem. An example is included to show the applicability of our results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a fractional Laplacian system with both concave-convex nonlinearities and sign-changing weight functions in bounded domains. With the help of the Nehari manifold, we prove that the system has at least two positive solutions when the pair of the parameters (λ, μ) belongs to a certain subset of ℝn. [ABSTRACT FROM AUTHOR]

n this paper, we introduce the notion of generalized Berinde nonexpansive mappings in metric spaces and show that it is weaker than the notion of Berinde nonexpansive mappings and stronger than the notion of semi-nonexpansive mappings. We also obtain the semiclosed principle, an endpoint theorem, and a common endpoint theorem for generalized Berinde nonexpansive mappings. Strong and Δ-convergence theorems of the Ishikawa iteration process for semi-nonexpansive mappings are also discussed. [ABSTRACT FROM AUTHOR]

In the present paper general theorems on a common fixed point for four mappings in dislocated metric space are proved. By the way, also results for three, two or one mapping are obtained. The assumptions are unified and compact. Numerous basic and sophisticated theorems can be derived from the facts presented in our paper. [ABSTRACT FROM AUTHOR]

In this paper we continue the study of those conditions that guarantee the existence of fixed points for variation mapping in the spirit of M.R. Taskovic. Concretely, we provide a general fixed point result for variation mappings defined in left-K-sequentially complete T1 quasimetric spaces in such a way that only lower semicontinuity from above is required instead of lower semicontinuity. We give examples that elucidate that the assumptions in the statement of our main result cannot be weakened. Moreover, it is shown that the CS-convergence condition by Taskovic implies left K-sequentially completeness and, thus, we retrieve the fixed point result for variation mappings in T1 quasi-metric spaces due to Taskovic. Furthermore, some fixed point theorems, among other Caristi type fixed point results, for variation mappings are derived as a particular case of our main result when several different quasi-metric notions of completeness are considered. Finally, we provide a characterization of left K-sequentially completeness for T1 quasi-metric spaces via variation mappings. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to introduce and study some viscosity-type proximal point algorithms for approximating a common solution of monotone inclusion problem and fixed point problem. We obtained strong convergence of the proposed algorithms to a common solution of minimization problem and fixed point problem for a generalized asymptotically nonexpansive mapping which is also a unique solution of some variational inequality problems in Hadamard spaces. Our results extend and complement some recent results in this direction. [ABSTRACT FROM AUTHOR]

In this paper, we prove several fixed point theorems on partially ordered Banach spaces, in which the considered mappings satisfy some order monotone conditions. In addition, if the considered mappings satisfy some continuity conditions, then some iterated schemes can be constructed to approximate the fixed points. Then we apply these theorems to prove an existence theorem of solutions to some Hammerstein integral equations. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to study the existence of solutions to semilinear evolution systems with nonlinear constraints. We establish new existence results using the fixed point principles of Perov and Schauder, combined with the technique that uses matrices with the spectral radius less than one and vector-valued norms. This vectorial approach is fruitful for the treating of systems in general and allows the system nonlinearities to behave independently as much as possible. Moreover, the constants from the Lipschitz or growth conditions are put into connection with the support of the nonlinear operators expressing the constraints. The paper extends and complements previous results from the literature. [ABSTRACT FROM AUTHOR]

This paper is generally concerned with the existence of solutions for a certain class of fractional differential inclusions with boundary conditions. By means a known fixed point theorem, some existence results are obtained. Utilizing some contractions including α-ϕ-Geraghty contraction, we examine the existence of solutions for some fractional differential inclusions. An example is given to illustrate the results. [ABSTRACT FROM AUTHOR]

In this paper, we extend to the case of product spaces, two generalizations of Maia fixed point theorem [Maia, Maria Grazia. Un'osservazione sulle contrazioni metriche. (Italian) Rend. Sem. Mat. Univ. Padova 40 1968 139{143] given by Rus I. A. in [Rus, Ioan A. Generalized contractions. Seminar on Fixed Point Theory, Babeş Bolyai Univ., Cluj-Napoca, 1983, Preprint nr. 3, pp. 1-130, 35] and [Rus, Ioan A. Basic problem for Maia's theorem. Seminar on Fixed Point Theory, Babeş Bolyai Univ., Cluj-Napoca, 1981, Preprint nr. 3, pp. 112-115]. Following the results in [Petruşel, A., Fredholm-Volterra integral equations and Maia's theorem, Seminar on Fixed Point Theory, Babeş Bolyai Univ., Cluj-Napoca, (1988), Preprint nr. 3, pp. 79{82], a theorem on the existence and uniqueness of solutions of Fredholm-Volterra integral equations, using a theorem of Maia type in product metric spaces, is proved. [ABSTRACT FROM AUTHOR]

In the paper, there were studied Caristi-like conditions that guaranteed existence of a minimum of a function on a metric space. For functions dependent on a parameter, there were obtained conditions for existence of a minimum for each value of the parameter. These results were applied to derive conditions for fixed point and coincidence point existence for mappings in metric spaces. For mappings dependent on a parameter, there were obtained conditions of coincidence point existence for each value of the parameter. [ABSTRACT FROM AUTHOR]

Recall from [2], that a mapping T : X 7→ X is called a Reich mapping if it satisfies for all x; yϵ X, d(Tx; Ty) ≤ ad(x; Tx) + bd(y; Ty) + cd(x; y), where a,b,c are nonnegative and satisfy a + b + c < 1. Alternatively, one could define a Reich mapping as follows: T : X 7→ X is called a Reich mapping if there exists a nonnegative constant k with k < 1 3 such that d(Tx; Ty) ≤ k[d(x; Tx)+d(y; Ty)+d(x; y)]. In the present paper, we address the following: How do we characterize Theorem 3 [2], when T is a non-self map? We show such a characterization is given by Theorem 3.1 or Corollary 3.2 in this paper. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the notion of complex valued fuzzy metric spaces. We prove some fixed point results of contractive mappings on complex valued fuzzy metric spaces. Some examples are presented to support the results proved herein. Our results extend various results in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper we present a new fixed point theorem in quasi-metric spaces which captures the spirit of Kleene's fixed point theorem. To this end, we explore the fundamental assumptions in the aforesaid result when we consider quasi-metric spaces endowed with the specialization partial order. Thus, we introduce an appropriate notion of order-completeness and order-continuity that ensure the existence of fixed point with distinguished properties. Moreover, some fixed point theorems are derived as a particular case of our main result when the self-mappings under consideration satisfy, in addition, any type of Banach contractive condition under different quasi-metric notions of completeness. [ABSTRACT FROM AUTHOR]

In this paper, we show that generalized Meir-Keeler type contractive definitions are strong enough to generate a fixed point but do not force the mapping to be continuous at the fixed point. Thus we provide more answers to the open question posed by B.E. Rhoades in the paper Contractive definitions and continuity, Contemporary Mathematics 72(1988), 233-245. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a general composite implicit scheme and a general composite explicit scheme for finding a solution of general system of variational inequalities in a real Hilbert space. We establish the strong convergence of these two general composite schemes to a solution of the general system of variational inequalities which is the unique solution of some variational inequality. Applications to variational inequalities are given. [ABSTRACT FROM AUTHOR]

In this paper we consider a pair of nonlinear matrix equations of the form X = Q1 + ..., Y = Q2 + ..., where Q1, Q2 are n x n Hermitian positive definite matrices, r1, r2 ∈ ℝ and prove the existence and uniqueness of positive definite solutions of these equations. We provide an algorithm to approach the solution. We present a coupled fixed point theorem for non-decreasing mapping and show that a particular case of our nonlinear matrix equations also can be solved by using the derived coupled fixed point theorem. Also we show that by replacing Y with Y-1 in first equation and X with X-1 in second equation and taking Q1 = Q2 and r1 = r2, the reduced system can be solved using the coupled fixed point theorem of Berinde [5]. [ABSTRACT FROM AUTHOR]

In this paper, we first define and study inverse-strongly monotone mappings in general metric spaces. Then, we prove the existence theorem of solutions for variational inequalities involving such mappings. Finally, we introduce an iterative process for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for inverse-strongly monotone mappings in CAT(0) metric spaces. [ABSTRACT FROM AUTHOR]

In this paper we give a quasi-metric version of Caristi's fixed point theorem by using mw-distances. Our theorem generalizes a recent result obtained by Karapinar and Romaguera in [7]. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of periodic points of asymptotically nonexpansive mappings defined on non-convex domains in uniformly convex Banach spaces. We also introduce the notion of firmly asymptotically nonexpansive mappings and prove the existence of fixed points of such mappings with non-convex domains. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of fixed point for relational endomorphisms. This class of mappings generalizes that of order and edge preserving mappings on posets and graphs respectively. As an application, we give a DeMarr-Type result for a family of Banach operator pairs in a binary relational system. [ABSTRACT FROM AUTHOR]